Αποτελέσματα Αναζήτησης
Write down the solution of the wave equation. utt = uxx. with ICs u (x, 0) = f (x) and ut (x, 0) = 0 using D’Alembert’s formula. Illustrate the nature of the solution by sketching the ux-profiles y = u (x, t) of the string displacement for t = 0, 1/2, 1, 3/2. Solution: D’Alembert’s formula is. x+t 1 .
Give one example of a transverse wave and one example of a longitudinal wave, being careful to note the relative directions of the disturbance and wave propagation in each. A sinusoidal transverse wave has a wavelength of 2.80 m.
K1. Vocabulary: amplitude, wavelength, wave number, phase, phase constant, wave function, wave speed, wave equation, harmonic function, sinusoidal wave, traveling wave, boundary conditions, ̄eld.
Sinusoidal waves. We have seen that the wave equation is solved by the d'Alembert solution y(x; t) = f(x ct) + g(x + ct). A particularly interesting option for f(u) and g(v) are sines and cosines. For example, we can choose. f(x ct) = C cos(k(x. ct) + '): (2.1) The sinusoidal wave is charaterised by.
Sinusoidal waves render the mathematical analysis, in terms of differential equations, straightforward and, for linear systems, provide a complete basis set from which any solution can be formed as a superposition – even if the system shows dispersion.
Problems for you to try: Complete the following practice problems. You MUST show ALL the work outlined in the steps in the example problems. 1. A wave with a frequency of 14 Hz has a wavelength of 3 meters. At what speed will this wave travel? 2. The speed of a wave is 65 m/sec. If the wavelength of the wave is 0.8 meters, what is the
In this module, we developed equations to model situations which were defined by information given about a function or by a sketch of a function. We used the graph of the function and the equation to obtain more information about the function.
